Abstract

Parametric max-stable processes are increasingly used to model spatial extremes. Since the dependence structure is specified for block maxima, the data used for inference are block maxima from all sites. To improve the estimation efficiency, we propose a two-step approach with composite likelihood that utilizes site-wise daily records in addition to block maxima. Besides the parameter estimation, there is no formal model checking and diagnosis method for spatial extremes modeling yet. Model diagnosis in practice has been informal and mostly based on visual checking tools such as residual plot and quantile-quantile plot. We proposed a goodness-of-fit test for max-stable processes based on the comparison between a nonparametric and a parametric estimator of the corresponding unknown multivariate Pickands dependence function. The proposed two-step procedure separates the estimation of marginal parameters and dependence parameters into two steps. The first step estimates the marginal parameters with an independence Likelihood by ignoring the spatial dependence. Given ithe marginal parameter estimates, the second step estimates the dependence parameters